I'm on an Ubuntu 14.04.4 LTS.
I just installed Intellij IDEA 2016.2 and got disapointed from the way my usual fonts (Dialog - for dialog windows and Monospaced for editor) are displayed. They are like completely different fonts in this new version. The same happened with 2016.1.3
This is very frustrating and I had to downgrade the Intellij IDEA to my previous version (2016.1) where the fonts are displaying OK.
Later I made some experiments and found out the the reason is the Open JDK version which is bundled with Idea and is used for starting it.
When starting Idea 2016.2 using Open JDK bundled in Idea 2016.1 there is no problem with rendering fonts.
So please fix the new Open JDK version bundled with Idea in order to render fonts properly.
PS: Find images with correct and wrong rendering: